How to add a Line between two moving Objects with Python?
This script will generate a simple single edge mesh, whose verts are hook connected to two pre-existing objects (the cylinders C1 and C2 in this example), which will also work simple animations of these two objects:

import bpy, bmesh
C = bpy.context

# Reference two cylinder objects
c1 = bpy.data.objects['C1']
c2 = bpy.data.objects['C2']

# Create new connector mesh and mesh object and link to scene
m = bpy.data.meshes.new('connector')

bm = bmesh.new()
v1 = bm.verts.new( c1.location )
v2 = bm.verts.new( c2.location )
e  = bm.edges.new([v1,v2])

bm.to_mesh(m)

o = bpy.data.objects.new( 'connector', m )
C.scene.collection.objects.link( o )

# Hook connector vertices to respective cylinders
for i, cyl in enumerate([ c1, c2 ]):
    bpy.ops.object.select_all( action = 'DESELECT' )
    cyl.select_set(True)
    o.select_set(True)
    C.view_layer.objects.active = o # Set connector as active

    # Select vertex
    bpy.ops.object.mode_set(mode='OBJECT')
    o.data.vertices[i].select = True    
    bpy.ops.object.mode_set(mode='EDIT')

    bpy.ops.object.hook_add_selob() # Hook to cylinder

    bpy.ops.object.mode_set(mode='OBJECT')
    o.data.vertices[i].select = False 

o.modifiers.new('Skin', 'SKIN')
bpy.ops.object.select_all( action = 'DESELECT' )